Observation of Entanglement-Dependent Two-Particle Holonomic Phase

Holonomic phases---geometric and topological---have long been an intriguing aspect of physics. They are ubiquitous, ranging from observations in particle physics to applications in fault tolerant quantum computing. However, their exploration in particles sharing genuine quantum correlations lack in observations. Here we experimentally demonstrate the holonomic phase of two entangled-photons evolving locally, which nevertheless gives rise to an entanglement-dependent phase. We observe its transition from geometric to topological as the entanglement between the particles is tuned from zero to maximal, and find this phase to behave more resilient to evolution changes with increasing entanglement. Furthermore, we theoretically show that holonomic phases can directly quantify the amount of quantum correlations between the two particles. Our results open up a new avenue for observations of holonomic phenomena in multi-particle entangled quantum systems.Comment: 8 pages, 6 figure

Bayesian astrostatistics: a backward look to the future

This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects that do not pass traditional detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in "Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed., Springer, New York, forthcoming in 2012), the inaugural volume for the Springer Series in Astrostatistics. Version 2 has minor clarifications and an additional referenc

Likelihood Analysis of Repeating in the BATSE Catalogue

I describe a new likelihood technique, based on counts-in-cells statistics, that I use to analyze repeating in the BATSE 1B and 2B catalogues. Using the 1B data, I find that repeating is preferred over non-repeating by 4.3:1 odds, with a well-defined peak at 5-6 repetitions per source. I find that the post-1B data are consistent with the repeating model inferred from the 1B data, after taking into account the lower fraction of bursts with well-determined positions. Combining the two data sets, I find that the odds favoring repeating over non-repeating are almost unaffected at 4:1, with a narrower peak at 5 repetitions per source. I conclude that the data sets are consistent both with each other and with repeating, and that for these data sets the odds favor repeating.Comment: 5 pages including 3 encapsulated figures, as a uuencoded, gzipped, Postscript file. To appear in Proc. of the 1995 La Jolla workshop ``High Velocity Neutron Stars and Gamma-Ray Bursts'' eds. Rothschild, R. et al., AIP, New Yor

Bayesian Analysis of the (Generalized) Chaplygin Gas and Cosmological Constant Models using the 157 gold SNe Ia Data

The generalized Chaplygin gas model (GCGM) contains 5 free parameters, here, they are constrained through the type Ia supernovae data, i.e., the ``gold sample'' of 157 supernovae data. Negative and large positive values for $\alpha$ are taken into account. The analysis is made by employing the Bayesian statistics and the prediction for each parameter is obtained by marginalizing on the remained ones. This procedure leads to the following predictions: $\alpha = - 0.75^{+4.04}_{-0.24}$, $H_0=65.00^{+1.77}_{-1.75}$, $\Omega_{k0} = - 0.77^{+1.14}_{-5.94}$, $\Omega_{m0} = 0.00^{+1.95}_{-0.00}$, $\Omega_{c0} = 1.36^{+5.36}_{-0.85}$, $\bar A = 1.000^{+0.000}_{-0.534}$. Through the same analysis the specific case of the ordinary Chaplygin gas model (CGM), for which $\alpha = 1$, is studied. In this case, there are now four free parameters and the predictions for them are: $H_0 = 65.01^{+1.81}_{-1.71}$, $\Omega_{k0} = - 2.73^{+1.53}_{-0.97}$, $\Omega_{m0} = 0.00^{+1.22}_{-0.00}$, $\Omega_{c0} = 1.34^{+0.94}_{-0.70}$, $\bar A = 1.000^{+0.000}_{-0.270}$. To complete the analysis the $\Lambda$CDM, with its three free parameters, is considered. For all these models, particular cases are considered where one or two parameters are fixed. The age of the Universe, the deceleration parameter and the moment the Universe begins to accelerate are also evaluated. The quartessence scenario, is favoured. A closed (and in some cases a flat) and accelerating Universe is also preferred. The CGM case $\alpha = 1$ is far from been ruled out, and it is even preferred in some particular cases. In most of the cases the $\Lambda$CDM is disfavoured with respect to GCGM and CGM.Comment: 23 pages, LaTeX 2e, 6 tables, 38 EPS figures, uses graphic

Avoiding selection bias in gravitational wave astronomy

When searching for gravitational waves in the data from ground-based gravitational wave detectors it is common to use a detection threshold to reduce the number of background events which are unlikely to be the signals of interest. However, imposing such a threshold will also discard some real signals with low amplitude, which can potentially bias any inferences drawn from the population of detected signals. We show how this selection bias is naturally avoided by using the full information from the search, considering both the selected data and our ignorance of the data that are thrown away, and considering all relevant signal and noise models. This approach produces unbiased estimates of parameters even in the presence of false alarms and incomplete data. This can be seen as an extension of previous methods into the high false rate regime where we are able to show that the quality of parameter inference can be optimised by lowering thresholds and increasing the false alarm rate.Comment: 13 pages, 2 figure

Bayesian Constraints on theta_{13} from Solar and KamLAND Neutrino Data

We present the results of a Bayesian analysis of solar and KamLAND neutrino data in the framework of three-neutrino mixing. We adopt two approaches for the prior probability distribution of the oscillation parameters Delta m^2_{21}, sin^2 theta_{12}, sin^2 theta_{13}: 1) a traditional flat uninformative prior; 2) an informative prior which describes the limits on sin^2 theta_{13} obtained in atmospheric and long-baseline accelerator and reactor neutrino experiments. In both approaches, we present the allowed regions in the sin^2 theta_{13} - Delta m^2_{21} and sin^2 theta_{12} - sin^2 theta_{13} planes, as well as the marginal posterior probability distribution of sin^2 theta_{13}. We confirm the 1.2 sigma hint of theta_{13} > 0 found in hep-ph/0806.2649 from the analysis of solar and KamLAND neutrino data. We found that the statistical significance of the hint is reduced to about 0.8 sigma by the constraints on sin^2 theta_{13} coming from atmospheric and long-baseline accelerator and reactor neutrino data, in agreement with arXiv:0808.2016.Comment: 21 pages. Final version published in Phys. Rev. D 80 (2009) 05300

Search for high-frequency periodicities in time-tagged event data from gamma ray bursts and soft gamma repeaters

We analyze the Time-Tagged Event (TTE) data from observations of gamma ray bursts (GRBs) and soft gamma repeaters (SGRs) by the Burst and Transient Source Experiment (BATSE). These data provide the best available time resolution for GRBs and SGRs. We have performed an extensive search for weak periodic signals in the frequency range 400 Hz to 2500 Hz using the burst records for 2203 GRBs and 152 SGR flares. The study employs the Rayleigh power as a test statistic to evaluate the evidence for periodic emissions. We find no evidence of periodic emissions from these events at these frequencies. In all but a very few cases the maximum power values obtained are consistent with what would be expected by chance from a non-periodic signal. In those few instances where there is marginal evidence for periodicity there are problems with the data that cast doubt on the reality of the signal. For classical GRBs, the largest Rayleigh power occurs in bursts whose TTE data appear to be corrupted. For SGRs, our largest Rayleigh power, with a significance of 1%, occurs in one record for SGR 1900+14 (at 2497 Hz), and in no other outbursts associated with this source; we thus consider it unlikely to represent detection of a real periodicity. From simulations, we deduce that the Rayleigh test would have detected significant oscillations with relative amplitude ~10% about half the time. Thus, we conclude that high frequency oscillations, if present, must have small relative amplitudes.Comment: 22 pages, 7 figures, submitted to Ap